2.) A business has budgeted to spend between \( \$ 500 \) and \( \$ 1000 \) a month on making advertising posters. It costs \( \$ 2 \) per poster, along with a monthly cost of \( \$ 300 \) for ink.

To determine how many advertising posters the business can produce each month within their budget, let's break down the costs and set up the appropriate inequalities. ### Given: - **Budget Range:** \$500 to \$1000 per month - **Cost per Poster:** \$2 - **Monthly Ink Cost:** \$300 Let \( x \) represent the number of posters produced in a month. ### Total Monthly Cost: The total cost consists of the cost of producing \( x \) posters plus the fixed monthly cost for ink. \[ \text{Total Cost} = 2x + 300 \] ### Setting Up the Inequalities: The total cost must be between \$500 and \$1000. Therefore, we can write the inequality as: \[ 500 \leq 2x + 300 \leq 1000 \] ### Solving the Inequalities: 1. **Subtract \$300 from all parts of the inequality:** \[ 500 - 300 \leq 2x \leq 1000 - 300 \] \[ 200 \leq 2x \leq 700 \] 2. **Divide all parts by 2 to solve for \( x \):** \[ \frac{200}{2} \leq x \leq \frac{700}{2} \] \[ 100 \leq x \leq 350 \] ### Conclusion: The business can produce **between 100 and 350 posters** each month while staying within their budget of \$500 to \$1000. - **Minimum Posters:** 100 - **Maximum Posters:** 350 ### Summary: \[ 100 \leq x \leq 350 \] This means that producing **at least 100 posters** and **no more than 350 posters** will ensure the business remains within its designated budget for advertising.